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Many mathematics students have difficulty making the transition from procedurally oriented courses such as calculus to the more conceptually oriented courses in which they subsequently enroll. What are some of the key "stumbling blocks" for students as they attempt to make this transition? How do differences in faculty expectations for students and student expectations for themselves contribute to the "transition dilemma?" What might faculty incorporate into students' learning experiences during the transition to help students better navigate the shift from procedural to conceptual, from concrete to abstract? This article offers some lessons learned in connection with these questions.

Mathematics majors' study of abstract algebra should provide these students with opportunities to connect what they are learning to their prior experiences with algebra in high school. This paper illustrates how such connections can be used to motivate the notion of binary operation and the axioms for a group.